One thing to be aware of when forming or interpreting condition indexes is that you need to center your $X$ variables first. Then your intercept will be uncorrelated with the rest of your variables and the condition index will be a measure of the multicollinearity amongst your variables. If you don't do this (and I'm guessing you didn't), the resulting condition index can say that there is a great deal of multicollinearity amongst your variables, but it is actually only for the intercept, which is not generally of interest and cannot be avoided anyway. To get a sense of this, it may help to read my answer here: Why does the standard error of the intercept increase the further $\bar x$ is from 0?